måndag 15 juni 2009

Is Quantum Computing Fiction?

In Chalmers Magasin for Alumni I read about research by Per Delsing and Göran Wendin on quantum computing using qu-bits, supposedly represented by superposed quantum states allowing computations, which are not possible on the computer we know using standard bits restricted to the two values 0 and 1.

Delsing and Wendin report that superposed states of 2-3 qu-bits have been realized but that 10 qu-bits represents a real challenge, not to speak of the thousands or millions needed for real quantum computing. Listen to Quantum Computing: Origins and Directions.

The basic question concerns superposition of quantum states, which is the question if the basic equation of quantum mechanics, Schrödinger's equation, is a linear equation.

I present reflections about this question in my knols on quantum mechanics, leading to the conclusion that Schrödinger's equation for a many-electron system is not linear, indicating that quantum computing is pure fiction. But maybe I am wrong. Would be interesting with some response from experts on quantum mechanics.

2 kommentarer:

Recent experiments seem to confirm that the Schroedinger equation is valid for extremely large numbers of particles, e.g. superpositions of macroscopic numbers of electrons circulating in two directions in a SQUID ring have been observed and the double slit experiment has been performed with carbon-60 molecules. Much of condensed matter theory depends on the existence of wavefunctions that involve large numbers of atoms and they don't seem to be having any problems reconciling theory with experiment at the moment. Therefore, I would say that some of the reasons to doubt macroscopic superpositions have definitely been refuted at this point.

On the other hand, none of these experiments involve fine-grained control of large quantum systems, which is what would be required for a quantum computer. It is still possible that something goes wrong with quantum theory before we reach this point, although you would be lucky to find any physicists betting that way. In any case, it would be extremely interesting if any fundamental limitations were found during the attempt to build a quantum computer, so I would argue that we win either way.

Thanks for comment. Any statement that Schrödingers equation is valid for a large number of electrons is questionable, since solutions to the equations cannot be determined analytically nor computationally. If solutions are unknown how can you verify that they fit with observations?